What types of 'esri layer' are you trying to add? Google Maps Android API does not support direct Esri data formats, e.g. shapefile, but you can added Google data types to ArcGIS Runtime SDK for Android, below is a sample of added a KML layer:
// Retrieve the map and initial extent from XML layout
mMapView = (MapView)findViewById(R.id.map);
// Create a new KML Layer
SpatialReference sr = SpatialReference.create(102100);
KMLLayer kmlLayer = new KMLLayer(url, sr);
// Add KML Layer to MapView;
mMapView.addLayer(kmlLayer);